A Kalman Filter approach is currently used to optimally
fit parameters of a fission model (such as the models in GNASH/TALYS etc.) to experimental
(n,f) cross sections and uncertainties. The high dimensionality of the parameter space can
often result in gradient-based optimization methods becoming fixated on local minima in their
search for optimal parameters. This can result in different optimal parameter sets being
returned by such techniques at different incident neutron energies -- a situation that one
would obviously wish to avoid for nuclear data applications. In a quest for robust estimation
methods, we explore optima in n-dimensional polyhedra. In particular, I will show application
to the evaluated Pu239(n,f) data in the ENDF/B-VII database over the incient neutron energy
range 0.1-8.5 MeV. Conditions under which the geometric methods are guaranteed to find global
optima will be discussed with a specific implementation using Chebyshev polynomials, and an
extension to evaluated data with uncertainties will be formulated to understand how covariance
matrices enter into this optimal estimation method.